Maximizing the Volume of a Cup Made from a Square Sheet of Paper ll

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration studies the maximization of the volume of a cup made from a square sheet of paper of size 12×12 cm. This is a new problem of mathematical origami presented by the authors.

Contributed by: Wataru Ogasa, Yuki Tomari, and Ryohei Miyadera (July 2011)
Open content licensed under CC BY-NC-SA



The volume of this 3D figure is . We look for the maximum value of for . By , we get as an approximate solution and .

According to the referee of the Journal Origami Society of Japan, maximizing the volume of a cup made from a square sheet of paper is a new problem proposed by the authors. Our previous research is presented in [2].

The origami wrapping problem, which has been studied by some mathematicians, looks for the biggest object that can be wrapped with a sheet of paper. See [1].


[1] M. L. Catalano-Johnson and D. Loeb, "Problem 10716: A Cubical Gift," American Mathematical Monthly, 108(1), 2001 pp. 81–82.

[2] W. Ogasa, T. Inoue, K. Nishimura, T. Nakaoka, D. Ikeda, A. Kanno, S. Nakamura, H. Matsui, T. Yamauchi, S. Utsuki, and R. Miyadera, "The Maximization of a Cup Made from a Square Sheet of Paper," Science of Origami, 1(1), 2011, in Japanese.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.